The hardwood species European oak, European chestnut and black locust are hardly used for engineering structures in their naturally grown shape, although such a use is generally possible. From forest thinnings these hardwoods are available as low-cost material to a certain extent and their durability and remarkable strength can fulfil the demands of robust timber structures. However, the irregular shape of naturally grown logs and the subsequent complexity of connections inhibit engineering applications. Thus, there is a gap between the potential of an available low-cost material and the possibility of a value-added application. In order to bridge this gap the present contribution aims first at giving basic ideas to make naturally grown logs more calculable and second at presenting a modular screw connection. Hence, compression tests on naturally grown logs, screw withdrawal tests and tests on screw connections were performed. Based on the experimental results, strength models for the compression capacity and the withdrawal resistance of screws were developed and a high strength and ductile connection type was designed. The findings of the work may widen the possibilities in the engineering design of timber structures made of naturally grown logs.